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      SUBROUTINE <a name="DLARZT.1"></a><a href="dlarzt.f.html#DLARZT.1">DLARZT</a>( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          DIRECT, STOREV
      INTEGER            K, LDT, LDV, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      DOUBLE PRECISION   T( LDT, * ), TAU( * ), V( LDV, * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="DLARZT.18"></a><a href="dlarzt.f.html#DLARZT.1">DLARZT</a> forms the triangular factor T of a real block reflector
</span><span class="comment">*</span><span class="comment">  H of order &gt; n, which is defined as a product of k elementary
</span><span class="comment">*</span><span class="comment">  reflectors.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  If STOREV = 'C', the vector which defines the elementary reflector
</span><span class="comment">*</span><span class="comment">  H(i) is stored in the i-th column of the array V, and
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     H  =  I - V * T * V'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  If STOREV = 'R', the vector which defines the elementary reflector
</span><span class="comment">*</span><span class="comment">  H(i) is stored in the i-th row of the array V, and
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     H  =  I - V' * T * V
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DIRECT  (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies the order in which the elementary reflectors are
</span><span class="comment">*</span><span class="comment">          multiplied to form the block reflector:
</span><span class="comment">*</span><span class="comment">          = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)
</span><span class="comment">*</span><span class="comment">          = 'B': H = H(k) . . . H(2) H(1) (Backward)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  STOREV  (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies how the vectors which define the elementary
</span><span class="comment">*</span><span class="comment">          reflectors are stored (see also Further Details):
</span><span class="comment">*</span><span class="comment">          = 'C': columnwise                        (not supported yet)
</span><span class="comment">*</span><span class="comment">          = 'R': rowwise
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the block reflector H. N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  K       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the triangular factor T (= the number of
</span><span class="comment">*</span><span class="comment">          elementary reflectors). K &gt;= 1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  V       (input/output) DOUBLE PRECISION array, dimension
</span><span class="comment">*</span><span class="comment">                               (LDV,K) if STOREV = 'C'
</span><span class="comment">*</span><span class="comment">                               (LDV,N) if STOREV = 'R'
</span><span class="comment">*</span><span class="comment">          The matrix V. See further details.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDV     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array V.
</span><span class="comment">*</span><span class="comment">          If STOREV = 'C', LDV &gt;= max(1,N); if STOREV = 'R', LDV &gt;= K.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  TAU     (input) DOUBLE PRECISION array, dimension (K)
</span><span class="comment">*</span><span class="comment">          TAU(i) must contain the scalar factor of the elementary
</span><span class="comment">*</span><span class="comment">          reflector H(i).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  T       (output) DOUBLE PRECISION array, dimension (LDT,K)
</span><span class="comment">*</span><span class="comment">          The k by k triangular factor T of the block reflector.
</span><span class="comment">*</span><span class="comment">          If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
</span><span class="comment">*</span><span class="comment">          lower triangular. The rest of the array is not used.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDT     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array T. LDT &gt;= K.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Further Details
</span><span class="comment">*</span><span class="comment">  ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Based on contributions by
</span><span class="comment">*</span><span class="comment">    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The shape of the matrix V and the storage of the vectors which define
</span><span class="comment">*</span><span class="comment">  the H(i) is best illustrated by the following example with n = 5 and
</span><span class="comment">*</span><span class="comment">  k = 3. The elements equal to 1 are not stored; the corresponding
</span><span class="comment">*</span><span class="comment">  array elements are modified but restored on exit. The rest of the
</span><span class="comment">*</span><span class="comment">  array is not used.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                                              ______V_____
</span><span class="comment">*</span><span class="comment">         ( v1 v2 v3 )                        /            \
</span><span class="comment">*</span><span class="comment">         ( v1 v2 v3 )                      ( v1 v1 v1 v1 v1 . . . . 1 )
</span><span class="comment">*</span><span class="comment">     V = ( v1 v2 v3 )                      ( v2 v2 v2 v2 v2 . . . 1   )
</span><span class="comment">*</span><span class="comment">         ( v1 v2 v3 )                      ( v3 v3 v3 v3 v3 . . 1     )
</span><span class="comment">*</span><span class="comment">         ( v1 v2 v3 )
</span><span class="comment">*</span><span class="comment">            .  .  .
</span><span class="comment">*</span><span class="comment">            .  .  .
</span><span class="comment">*</span><span class="comment">            1  .  .
</span><span class="comment">*</span><span class="comment">               1  .
</span><span class="comment">*</span><span class="comment">                  1
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                                                        ______V_____
</span><span class="comment">*</span><span class="comment">            1                                          /            \
</span><span class="comment">*</span><span class="comment">            .  1                           ( 1 . . . . v1 v1 v1 v1 v1 )
</span><span class="comment">*</span><span class="comment">            .  .  1                        ( . 1 . . . v2 v2 v2 v2 v2 )
</span><span class="comment">*</span><span class="comment">            .  .  .                        ( . . 1 . . v3 v3 v3 v3 v3 )
</span><span class="comment">*</span><span class="comment">            .  .  .
</span><span class="comment">*</span><span class="comment">         ( v1 v2 v3 )
</span><span class="comment">*</span><span class="comment">         ( v1 v2 v3 )
</span><span class="comment">*</span><span class="comment">     V = ( v1 v2 v3 )
</span><span class="comment">*</span><span class="comment">         ( v1 v2 v3 )
</span><span class="comment">*</span><span class="comment">         ( v1 v2 v3 )
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      DOUBLE PRECISION   ZERO
      PARAMETER          ( ZERO = 0.0D+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I, INFO, J
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           DGEMV, DTRMV, <a name="XERBLA.131"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.134"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.135"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Check for currently supported options
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      IF( .NOT.<a name="LSAME.142"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( DIRECT, <span class="string">'B'</span> ) ) THEN
         INFO = -1
      ELSE IF( .NOT.<a name="LSAME.144"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( STOREV, <span class="string">'R'</span> ) ) THEN
         INFO = -2
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.148"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DLARZT.148"></a><a href="dlarzt.f.html#DLARZT.1">DLARZT</a>'</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span>      DO 20 I = K, 1, -1
         IF( TAU( I ).EQ.ZERO ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           H(i)  =  I
</span><span class="comment">*</span><span class="comment">
</span>            DO 10 J = I, K
               T( J, I ) = ZERO
   10       CONTINUE
         ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           general case
</span><span class="comment">*</span><span class="comment">
</span>            IF( I.LT.K ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)'
</span><span class="comment">*</span><span class="comment">
</span>               CALL DGEMV( <span class="string">'No transpose'</span>, K-I, N, -TAU( I ),
     $                     V( I+1, 1 ), LDV, V( I, 1 ), LDV, ZERO,
     $                     T( I+1, I ), 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              T(i+1:k,i) = T(i+1:k,i+1:k) * T(i+1:k,i)
</span><span class="comment">*</span><span class="comment">
</span>               CALL DTRMV( <span class="string">'Lower'</span>, <span class="string">'No transpose'</span>, <span class="string">'Non-unit'</span>, K-I,
     $                     T( I+1, I+1 ), LDT, T( I+1, I ), 1 )
            END IF
            T( I, I ) = TAU( I )
         END IF
   20 CONTINUE
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="DLARZT.182"></a><a href="dlarzt.f.html#DLARZT.1">DLARZT</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

</pre>

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